About Bayesian formula- P(WlX)=P(XlW)*P(W)/P(X) What is the correct description?

Question

Options

• AP(WIX) is a prior probability
• BP(XIW) 1s a conditional probability
• CP(W) is the posterior probability
• DP(X) is the posterior probability

• A
  13% (3)
• B
  78% (18)
• C
  4% (1)
• D
  4% (1)

Explanation

B is correct because P(X|W) is literally defined as a conditional probability - the probability of X given W - and in Bayesian terminology it also serves as the likelihood of the evidence.

Why the distractors are wrong:

• A is wrong: P(W|X) is the posterior probability - it's the updated belief about W after observing X, not the prior.
• C is wrong: P(W) is the prior probability - your belief about W before any evidence is observed.
• D is wrong: P(X) is the marginal probability (or normalizing constant/evidence), not the posterior.

Memory tip: Think of the formula as a belief-update machine - Prior × Likelihood ÷ Evidence = Posterior. Map each term: P(W) = Prior, P(X|W) = Likelihood, P(X) = Evidence, P(W|X) = Posterior. The only term that is simply "conditional" by name and role is P(X|W), making B unambiguously correct.

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